On the generalization of the Salem test

The assertion that the Salem test 5] for the uniform convergence of a trigonometric Fourier series is improvable, is proved. In particular, an example of a continuous function, which does not fulfill the condition of the Salem test but satisfies the condition of the generalized Salem test 10], is constructed.Besides, the theorem which improves Golubov’s 3,4] result for continuous functions of two variables, is given.